Alexander's family lived in Alexandria, Egypt. Although nothing is known about Alexander's parents, they must have been noble and wealthy, because Josephus reports that Alexander "surpassed all his fellow citizens both in ancestry and in wealth." (Antiquities 20.100). Philo was Alexander's older brother.

At some unknown date, Alexander was appointed Alabarch of Alexandria. The alabarch was a magistrate responsible for customs in Alexandria.[5][6] Later Alexander became an administrator for the extensive land estates in Egypt, owned by Antonia Minor. Antonia Minor was a Roman noblewoman, who was the niece of Emperor Augustus and the youngest daughter of the triumvirMark Antony. Alexander had been a long-time friend of Antonia Minor’s youngest child, the future Emperor Claudius.[citation needed]

As an indication of Alexander’s great wealth, he had nine gates at the Second Temple in Jerusalem "overlaid with massive plates of silver and gold." (War, 5.205)[7]

In around 32-35 AD, the Herodian Agrippa I was indebted to Rome for 300,000 pieces of silver. (Evans, pp. 578–9) Agrippa escaped Judea and sailed to Alexandria to beg Alexander to loan him 200,000 drachmas. Alexander refused to give the money directly to Agrippa, but agreed to loan Agrippa's wife Cypros the money because Alexander "marvelled at her love of her husband and all her other good qualities." (Antiquities, 18.159-160)

Sometime between 37 and 41 AD, the Emperor Caligula ordered Alexander to be imprisoned in Rome for an unknown reason. This could be connected to Philo’s embassy to Caligula in Rome in 39/40. After the death of Caligula in 41, his paternal uncle Claudius became Emperor and he immediately released Alexander from prison. Josephus wrote that Alexander was "an old friend of [Claudius], who had acted as guardian for his mother Antonia." (Antiquities, 19.276)